Details

analyze594.0ms (6.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
12.5%	87.4%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
62.4%	31.2%	6.3%	7
62.4%	31.2%	6.3%	8
62.4%	28.1%	9.5%	9
62.4%	28.1%	9.5%	10
62.4%	26.5%	11%	11
62.4%	26.5%	11%	12
62.4%	25.8%	11.8%	13
62.4%	25.8%	11.8%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample268.0ms (3%)

Algorithm

1×

intervals

Results

75.0ms	139×	body	1024	valid
63.0ms	50×	body	1024	invalid
16.0ms	64×	body	512	valid
10.0ms	10×	body	2048	valid
7.0ms	88×	body	128	invalid
5.0ms	21×	body	512	invalid
4.0ms	29×	body	256	valid
2.0ms	12×	body	256	invalid
1.0ms	14×	body	128	valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify113.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

454×	`fma-def_binary64`
444×	`times-frac_binary64`
419×	`sub-neg_binary64`
365×	`distribute-rgt-neg-in_binary64`
340×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	23	18
2	49	18
3	106	18
4	225	17
5	449	17
6	962	17
7	1713	17
8	3588	17
9	4282	17
10	4773	17
11	4923	17
12	4957	17
13	4748	17

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

45.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	45.0b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Compiler

Compiled 50 to 35 computations (30% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	4.0b	(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

series20.0ms (0.2%)

Counts

2 → 32

Calls

2 calls:

18.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
2.0ms	(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
27×	`prod-diff_binary64`
25×	`add-cube-cbrt_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 80

Calls

2 calls:

8.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
5.0ms	(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

simplify94.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

584×	`fma-neg_binary64`
356×	`cancel-sign-sub-inv_binary64`
302×	`distribute-rgt-in_binary64`
277×	`associate-r_binary64`
274×	`associate-l_binary64`

Counts

112 → 124

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	225	2646
1	547	2347
2	2043	2132
3	4415	2127
4	4897	2127

prune70.0ms (0.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	122	3	125

Error

0.1b

Counts

125 → 3

Alt Table

Status	Error	Program
✓	45.0b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
	0.2b	(.f64 (.f64 1/2 (sin.f64 re)) (fma.f64 (pow.f64 im 5) -1/60 (fma.f64 (pow.f64 im 3) -1/3 (*.f64 -2 im))))
▶	0.2b	(neg.f64 (fma.f64 im (sin.f64 re) (.f64 (sin.f64 re) (+.f64 (.f64 1/6 (pow.f64 im 3)) (*.f64 1/120 (pow.f64 im 5))))))

Compiler

Compiled 3244 to 1150 computations (64.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 1/120 (pow.f64 im 5))
✓	0.1b	(.f64 (sin.f64 re) (+.f64 (.f64 1/6 (pow.f64 im 3)) (*.f64 1/120 (pow.f64 im 5))))
✓	0.1b	(fma.f64 im (sin.f64 re) (.f64 (sin.f64 re) (+.f64 (.f64 1/6 (pow.f64 im 3)) (*.f64 1/120 (pow.f64 im 5)))))
✓	0.1b	(*.f64 1/6 (pow.f64 im 3))

series73.0ms (0.8%)

Counts

4 → 48

Calls

4 calls:

35.0ms	(fma.f64 im (sin.f64 re) (.f64 (sin.f64 re) (+.f64 (.f64 1/6 (pow.f64 im 3)) (*.f64 1/120 (pow.f64 im 5)))))
32.0ms	(.f64 (sin.f64 re) (+.f64 (.f64 1/6 (pow.f64 im 3)) (*.f64 1/120 (pow.f64 im 5))))
3.0ms	(*.f64 1/120 (pow.f64 im 5))
3.0ms	(*.f64 1/6 (pow.f64 im 3))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
22×	`associate-r_binary64`
16×	`add-exp-log_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`

Counts

4 → 94

Calls

4 calls:

6.0ms	(.f64 (sin.f64 re) (+.f64 (.f64 1/6 (pow.f64 im 3)) (*.f64 1/120 (pow.f64 im 5))))
6.0ms	(*.f64 1/6 (pow.f64 im 3))
4.0ms	(*.f64 1/120 (pow.f64 im 5))
0.0ms	(fma.f64 im (sin.f64 re) (.f64 (sin.f64 re) (+.f64 (.f64 1/6 (pow.f64 im 3)) (*.f64 1/120 (pow.f64 im 5)))))

simplify122.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

430×	`cancel-sign-sub-inv_binary64`
374×	`distribute-rgt-in_binary64`
351×	`distribute-lft-in_binary64`
327×	`fma-neg_binary64`
256×	`associate-r_binary64`

Counts

142 → 156

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	226	2918
1	577	2607
2	2137	2544
3	4616	2543
4	4979	2543
5	4966	2543

prune174.0ms (2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	153	3	156
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	154	5	159

Error

0.1b

Counts

159 → 5

Alt Table

Status	Error	Program
✓	0.2b	(neg.f64 (fma.f64 im (sin.f64 re) (.f64 (sin.f64 re) (+.f64 (.f64 1/6 (pow.f64 im 3)) (*.f64 1/120 (pow.f64 im 5))))))
	27.2b	(neg.f64 (.f64 (sqrt.f64 (.f64 (sin.f64 re) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im)))) (sqrt.f64 (*.f64 (sin.f64 re) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im))))))
	1.2b	(neg.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 im (sin.f64 re) (.f64 (sin.f64 re) (+.f64 (.f64 1/6 (pow.f64 im 3)) (.f64 1/120 (pow.f64 im 5)))))) (cbrt.f64 (fma.f64 im (sin.f64 re) (.f64 (sin.f64 re) (+.f64 (.f64 1/6 (pow.f64 im 3)) (.f64 1/120 (pow.f64 im 5))))))) (cbrt.f64 (fma.f64 im (sin.f64 re) (.f64 (sin.f64 re) (+.f64 (.f64 1/6 (pow.f64 im 3)) (*.f64 1/120 (pow.f64 im 5))))))))
✓	45.0b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
▶	0.2b	(neg.f64 (*.f64 (sin.f64 re) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im))))

Compiler

Compiled 4680 to 3210 computations (31.4% saved)

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im))
✓	0.1b	(*.f64 (sin.f64 re) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im)))

series36.0ms (0.4%)

Counts

2 → 36

Calls

2 calls:

32.0ms	(*.f64 (sin.f64 re) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im)))
4.0ms	(fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

2 → 32

Calls

2 calls:

3.0ms	(*.f64 (sin.f64 re) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im)))
0.0ms	(fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im))

simplify71.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

773×	`fma-neg_binary64`
743×	`fma-def_binary64`
424×	`distribute-rgt-in_binary64`
408×	`distribute-lft-in_binary64`
271×	`associate--l+_binary64`

Counts

68 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	112	1648
1	301	1502
2	1228	1469
3	4708	1469
4	5360	1469

prune90.0ms (1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	66	5	71
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	67	9	76

Error

0.0b

Counts

76 → 9

Alt Table

Status	Error	Program
	30.6b	(neg.f64 (.f64 (sqrt.f64 (sin.f64 re)) (.f64 (sqrt.f64 (sin.f64 re)) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im)))))
✓	0.2b	(neg.f64 (fma.f64 im (sin.f64 re) (.f64 (sin.f64 re) (+.f64 (.f64 1/6 (pow.f64 im 3)) (*.f64 1/120 (pow.f64 im 5))))))
	31.1b	(neg.f64 (.f64 (.f64 (sin.f64 re) (sqrt.f64 (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im)))) (sqrt.f64 (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im)))))
	1.3b	(neg.f64 (.f64 (.f64 (sin.f64 re) (*.f64 (cbrt.f64 (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im))) (cbrt.f64 (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im))))) (cbrt.f64 (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im)))))
▶	1.2b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 re)) (cbrt.f64 (sin.f64 re))) (*.f64 (cbrt.f64 (sin.f64 re)) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im)))))
	27.2b	(neg.f64 (.f64 (sqrt.f64 (.f64 (sin.f64 re) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im)))) (sqrt.f64 (*.f64 (sin.f64 re) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im))))))
	36.1b	(neg.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 re) (sin.f64 re)) (sin.f64 re)) (.f64 (*.f64 (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im)) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im))) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im))))))
✓	45.0b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	0.2b	(neg.f64 (*.f64 (sin.f64 re) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im))))

Compiler

Compiled 2177 to 1526 computations (29.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 (sin.f64 re)) (cbrt.f64 (sin.f64 re))) (*.f64 (cbrt.f64 (sin.f64 re)) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im))))
✓	0.3b	(*.f64 (cbrt.f64 (sin.f64 re)) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im)))
✓	0.5b	(*.f64 (cbrt.f64 (sin.f64 re)) (cbrt.f64 (sin.f64 re)))
✓	0.6b	(cbrt.f64 (sin.f64 re))

series687.0ms (7.7%)

Counts

4 → 72

Calls

4 calls:

238.0ms	(*.f64 (cbrt.f64 (sin.f64 re)) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im)))
234.0ms	(*.f64 (cbrt.f64 (sin.f64 re)) (cbrt.f64 (sin.f64 re)))
182.0ms	(cbrt.f64 (sin.f64 re))
33.0ms	(.f64 (.f64 (cbrt.f64 (sin.f64 re)) (cbrt.f64 (sin.f64 re))) (*.f64 (cbrt.f64 (sin.f64 re)) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im))))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
23×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 109

Calls

4 calls:

7.0ms	(.f64 (.f64 (cbrt.f64 (sin.f64 re)) (cbrt.f64 (sin.f64 re))) (*.f64 (cbrt.f64 (sin.f64 re)) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im))))
7.0ms	(*.f64 (cbrt.f64 (sin.f64 re)) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im)))
5.0ms	(*.f64 (cbrt.f64 (sin.f64 re)) (cbrt.f64 (sin.f64 re)))
1.0ms	(cbrt.f64 (sin.f64 re))

simplify121.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

485×	`cancel-sign-sub-inv_binary64`
479×	`unswap-sqr_binary64`
403×	`associate-r_binary64`
377×	`associate-l_binary64`
322×	`fma-neg_binary64`

Counts

181 → 193

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	281	4082
1	771	3548
2	3125	3495
3	4827	3486
4	5028	3486

prune287.0ms (3.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	238	3	241
Fresh	1	4	5
Picked	1	0	1
Done	0	3	3
Total	240	10	250

Error

0.0b

Counts

250 → 10

Alt Table

Status	Error	Program
	30.6b	(neg.f64 (.f64 (sqrt.f64 (sin.f64 re)) (.f64 (sqrt.f64 (sin.f64 re)) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im)))))
✓	0.2b	(neg.f64 (fma.f64 im (sin.f64 re) (.f64 (sin.f64 re) (+.f64 (.f64 1/6 (pow.f64 im 3)) (*.f64 1/120 (pow.f64 im 5))))))
	1.2b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 re)) (cbrt.f64 (sin.f64 re))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (sin.f64 re)) (cbrt.f64 (sin.f64 re)))) (*.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im))))))
	36.1b	(neg.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 re) (sin.f64 re)) (sin.f64 re)) (.f64 (*.f64 (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im)) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im))) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im))))))
	31.1b	(neg.f64 (.f64 (.f64 (sin.f64 re) (sqrt.f64 (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im)))) (sqrt.f64 (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im)))))
	3.6b	(neg.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 re) 2)) (.f64 (cbrt.f64 (sin.f64 re)) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im)))))
	27.2b	(neg.f64 (.f64 (sqrt.f64 (.f64 (sin.f64 re) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im)))) (sqrt.f64 (*.f64 (sin.f64 re) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im))))))
✓	45.0b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
	31.3b	(neg.f64 (.f64 (cbrt.f64 (sin.f64 re)) (.f64 (pow.f64 (sin.f64 re) 2/3) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im)))))
✓	0.2b	(neg.f64 (*.f64 (sin.f64 re) (fma.f64 1/120 (pow.f64 im 5) (fma.f64 1/6 (pow.f64 im 3) im))))

Compiler

Compiled 8090 to 4454 computations (44.9% saved)

regimes697.0ms (7.8%)

Accuracy

Total 0.8b remaining (93.2%)

Threshold costs 0.8b (93.2%)

Counts

102 → 1

Compiler

Compiled 16185 to 10706 computations (33.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	29
1	24	29
2	26	29
3	27	29
4	27	29

end1.0ms (0%)

Compiler: Compiled 21 to 15 computations (28.6% saved)

sample5.3s (59.2%)

Algorithm

1×

intervals

Results

2.4s	4074×	body	1024	valid
757.0ms	1961×	body	1024	invalid
558.0ms	2102×	body	512	valid
218.0ms	947×	body	512	invalid
205.0ms	2620×	body	128	invalid
167.0ms	1026×	body	256	valid
155.0ms	195×	body	2048	valid
70.0ms	466×	body	256	invalid
54.0ms	603×	body	128	valid

Compiler

Compiled 306 to 218 computations (28.8% saved)

Details

analyze594.0ms (6.7%)

sample268.0ms (3%)

simplify113.0ms (1.3%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series20.0ms (0.2%)

rewrite19.0ms (0.2%)

simplify94.0ms (1.1%)

prune70.0ms (0.8%)

localize12.0ms (0.1%)

series73.0ms (0.8%)

rewrite20.0ms (0.2%)

simplify122.0ms (1.4%)

prune174.0ms (2%)

localize12.0ms (0.1%)

series36.0ms (0.4%)

rewrite5.0ms (0.1%)

simplify71.0ms (0.8%)

prune90.0ms (1%)

localize15.0ms (0.2%)

series687.0ms (7.7%)

rewrite26.0ms (0.3%)

simplify121.0ms (1.4%)

prune287.0ms (3.2%)

regimes697.0ms (7.8%)

simplify2.0ms (0%)

end1.0ms (0%)

sample5.3s (59.2%)

Profiling